Some mathematical problems in inverse potential scattering
Some new problems in spectral optimization
We present some new problems in spectral optimization. The first one consists in determining the best domain for the Dirichlet energy (or for the first eigenvalue) of the metric Laplacian, and we consider in particular Riemannian or Finsler manifolds, Carnot-Carathéodory spaces, Gaussian spaces. The second one deals with the optimal shape of a graph when the minimization cost is of spectral type. The third one is the optimization problem for a Schrödinger potential in suitable classes.
Some new results in spectral and scattering theory of differential operators on
Some non-local problems for the parabolic-hyperbolic type equation with non-characteristic line of changing type
In this work two non-local problems for the parabolic-hyperbolic type equation with non-characteristic line of changing type are considered. Unique solvability of these problems is proven. The uniqueness of the solution is proven by the method of energy integrals and the existence is proven by the method of integral equations.
Some observations on the first eigenvalue of the -Laplacian and its connections with asymmetry.
Some problems in inverse scattering theory
Some properties of eigenfunctions of linear pencils and applications to mixed type operator-differential equations
In the first part of the paper we study some properties of eigenelements of linear selfadjoint pencils Lu = λBu. In the second part we apply these results to the investigation of some boundary value problems for mixed type second order operator-differential equations.
Some properties of Legendre functions and related applications.
Some properties of Riesz means and spectral expansions. (With an appendix by R. A. Gustafson).
Some remarks on a result of Talenti
Some remarks on double-wells in one and three dimensions
Some remarks on eigenfunction expansions for Schrödinger operators with non-local potentials.
Some remarks on infinite-dimensional nonlinear elliptic problems.
Some remarks on the multi-dimensional Borg-Levinson theorem
Some remarks on the number of solutions of some nonlinear elliptic problems
Some remarks on the Weyl asymptotics by the approximate spectral projection method
In questo lavoro studiamo il resto relativo della formula asintotica per gli autovalori di un operatore differenziale in , ottenuta mediante il metodo delle proiezioni spettrali approssimate ([3], Theorem 6.2). In un primo tempo diamo un controesempio di un operatore di Schrödinger con potenziale a crescita algebrica, per il quale il resto non è limitato. Quindi specifichiamo alcune condizioni addizionali da imporre all'operatore in modo da avere un resto infinitesimo.
Some Remarks on Transmutation, Scattering Theory, and Special Functions.
Some results on eigenfunctions on symmetric spaces and eigenspace representations.
Some solved and unsolved canonical problems of diffraction theory
Some stability properties for minimal solutions of .